Question

If α and β are the zeroes of the quadratic polynomial f(t) = t² - 5t + 3 , find the value of a⁴β³ + α³β⁴

Answer 1

Hey There,

Here, we are given:
$f(t)=t^2-5t+3$

$\alpha$ and $\beta$ are zeros.

So,
Sum of zeros is:

$\alpha + \beta =-\frac{(-5)}{1} = 5 \\ \\ \\ \implies \boxed{\alpha + \beta = 5}$


Also, Product of Zeros is:

$\alpha \beta = \frac{3}{1} = 3 \\ \\ \\ \implies \boxed{\alpha \beta = 3}$


Now, we can solve your question as follows:

$\alpha^4 \beta^3 + \alpha^3 \beta^4 \\ \\ \\ = \alpha^3 \beta^3 (\alpha + \beta) \\ \\ \\ = 3^3 (5) \\ \\ \\ = 27 \times 5 \\ \\ \\ = \textbf{135}$


Thus, your answer is 135



Hope it helps
Purva
Brainly Community

Answer 2

Answer:

It is given that $\alpha$ and $\beta$ are the zeroes or roots of the quadriatic polynomial f(t) = t²-4t+3

∴ $\alpha$+$\beta$ = -b/a = -(-4 )/1 =4 also $\alpha$$\beta$ = c/a = 3/1=3

∴$\alpha$^4$\beta$³ + $\beta$^4³ = $\alpha$³$\beta$³ ($\alpha$+$\beta$) =(3)³. 4⇒ 27.4⇒108.

Hope this will help you.

For Brainly Community

By CHINMAY

Step-by-step explanation: